MATHS M.C.Q. [1 Marks Each]

$2\ km 35m = 2.035\ km$
($\because$ $1000m = 1\ km)$

given that, $617.0000 + 6.0170 + 0.6170 + 6.0017 = 629.6357$

$5$ is in the thousandth place.
$0.04532=\frac{4}{100}+\frac{5}{1000}+\frac{3}{10000}+\frac{2}{100000}$

$\therefore9.02=5.7=3.32$

Expanded form of $78.059$ is $7+8+0+\frac{5}{100}+\frac{9}{1000}$

$626.235$
There are two 6s in this number, one at Hundreds place and other at Ones place.
$\Rightarrow $ Place values of $6 = 6 \times 100$ and $6 \times 1$
Difference $= 600 - 6 = 594$

To find the percent of a given number, we will multiply it with $100$
Let the number in decimal be $x$
The number in percent is $12\frac{1}{4} = \frac{49}{4}$
When converted to percent, the number becomes $\text{x}\times100= \frac{49}{4}$'
$\Rightarrow \text{x}=\dfrac{49}{400} =0.1225$

Expanded form of $920831$
$900000 + 20000 + 800 + 30 + 1$

$32.000 - 27.091 = 4.909$

$4+\frac{3}{100}=\frac{400+3}{100}=4.03$

$\frac{7}{100}$ is equal to $0.07$. Since the denominator is $100$, we have to mark the decimal such that $7$ is in the hundredth place.

$600.065 = 600 + 0.65 + 0.001$

To add 3 decimal numbers of different decimal values we pick the number with the highest decimal
value and expand all the other numbers to the same value by adding $0$ after the decimal point.
$0.300 + 0.030 + 0.003 = 0.333$

The fraction $\frac{9}{10}$ in decimal form is $0.9$

Difference in pocket money of Madhu and Srinu $= 4.25 - 3.75 = 0.50$
Difference in one week $= 0.50 \times 7 = 3.50$

$4\frac{7}{8}=4+\frac{7\times125}{8\times125}$
$=4+\frac{875}{1000}$
$=4+0.875$
$=4.875$

To write it as a decimal we divide the numerator from the denominator $\frac{9}{1000}=0.009$
So, $0.009$ is the decimal representation for $\frac{9}{1000}$

$2.5 + 3.05 - 4.005$
$= 5.55 - 4.005$
$= 1.545$

$2\ m \ 5\ cm = 2.05\ m$

To round to the nearest tenth, write down the number with a decimal point, and find the tenths place directly to the right of the decimal.
Then, to the right of the tenths place, look at the number in the hundredths place.
In $6050.287$ the number in the hundredths is $2.2.$
So, $6050.287$ rounded to the nearest tenths will be $6050.3$

The sum of two numbers $= 31.021$
One of the numbers $= 11.560$
Other number $= 31.021 - 11.560 = 19.461$

The value of $2.\overline{6}-1.\overline{9}$ is
$=\Big(2+\frac{6}{9}\Big)-\Big(1+\frac{9}{9}\Big)$
$=\frac{6}{9}=0.\overline{6}$

We know that $100\ cm = 1m.$
Therefore, $1\text{cm}=\frac{1}{100}\text{m}=0.01\text{m.}$

Converting into like decimals:
$\ \ \ 5.01\\ \underline{-3.60}\\ \underline{\ \ \ 1.41}$

$1\text{cm}=\frac{1}{100}\text{m}$
$=0.01$

Since the denominator is $1000$, we have to mark the decimal such that $4$ is in the thousandth place.

$\frac{3}{10}=0.3$ (since the denominator is $10$, we need to mark the decimal such that $3$ is in the tenth place).
$\frac{5}{100}=0.05$ (since the denominator is $100$, we need to mark the decimal such that $5$ is in the hundredth place).
Therefore, $2+\frac{3}{10}+\frac{5}{100}=2+0.3+0.05$
$=2.35$

$\frac{16}{1000}=0.016$

$\begin{aligned}
&\begin{aligned}
& 1 \\
& 12.56 \\
& +0.50 \\
& \hline 13.06 \\
& \\
& 13.060 \\
& +0.003 \\
& \hline 13.063
\end{aligned}\\
&\text { Option A is correct. }
\end{aligned}$

$95.75 \times 0.2554 = 24.45455$
Sum of decimal places $= 7$ Since the last digit to the extreme right will be zero
(since $5 \times 4 = 20)$, so there will be $5$ significant digits to the right of the decimal point.

$\frac{4}{20}=\frac{4}{20}\times\frac{5}{5}=\frac{20}{100}=0.20$

$2\frac{1}{25}=2+\frac{1}{25}$
$=2+\frac{1\times4}{25\times4}$
$=2+\frac{4}{100}$
$=2+0.04$
$=2.04$

For obtaining the sum of decimal numbers with different decimal values we expand the decimal
values of all the numbers with respect to the number with the highest decimal value.
Because the number with the largest decimal places is $72.985$ with $3$ decimal places, we expand all numbers up to $3$ decimal places.$1.800 + 16.300 + 72.985 = 91.085$

Converting decimal into fraction $0.6=\frac{6}{10}$

If we arrange the given numbers in ascending order, we get $0.015 < 0.105 < 0.15 < 0.501$

According to number system, every fraction in $\frac{\text{P}}{\text{q}}$ form can be converted into decimal number. and vice versa.

A decimal number is read by first reading the whole number part, then the decimal point and the digits of the decimal part one by one.
Hence, the decimal number $9.6$ is read as Nine point six

$\because 0.4 + 0.004 + 4.4$
$= 4.804$

$2+\frac{3}{10}+\frac{4}{100}$
$=2+0.3+0.04$
$=2.34$

Among $2.600, 2.006, 2.660,2.080, 2.660$ is the largest.

We know that to add numbers with different decimal places we expand all the numbers to the same decimal places by expanding zeroes.
So, the sum of $0.5, 12.56$ and $0.003$ is
$0.500 + 12.560 + 0.003 = 13.063$

$=2.06$
$(2\times1)+\Big(6\times\frac{1}{100}\Big)$
$=2+\frac{6}{100}$

$\because 3.5 + 4.05 - 6.005$
$= 3.500 + 4.050 - 6.005$
$= 7.550 - 6.005$
$= 1.545$

The fraction $\frac{3}{1000}$ in decimal form is $0.003.$

$\frac{3}{100}=0.03$ (here, we have the denominator $100,$ so we mark the decimal such that $3$ is in the hundredth place).
$\frac{5}{10000}=0.0005$ (here, we have the denominator $10000$, so we mark the decimal such that $5$ is in the ten thousandth place).
Therefore, $\frac{3}{100}+\frac{5}{10000}=0.03+0.0005$
$=0.0305$

Distance between points $= 4.5 - (-2.3) = 6.8$

To find the percent of a given number, we will multiply it with $100.$
Let the number in decimal be $x$
When converted to percent, the number becomes $x \times 100 = 62.9$
$\Rightarrow\text{x}=\frac{62.9}{100}$
$\Rightarrow\text{x}=0.629$

Converting all the given decimals into like decimals:
$2.600, 2.006, 2.660$ and $2.080$
Among these given like decimals, $2.660$ is the largest.

$\frac{4}{100}+\frac{7}{10000}$
$=0.04+0.0007$
$=0.0407$

$\frac{5}{10}+\frac{3}{100}$
$=0.5+0.03$
$=0.53$

$36.2<\text{br}/>\Rightarrow 36+0.2 = \frac {362} {10} = 36\frac {2} {10}$

When the prime factorization of the denominator of a fraction has only factors of $2$ and factors of $5$, then the number is a terminating decimal. If there are prime factors in the denominator other than $2$ or $5$, then the decimals repeat.

$2\frac{19}{100}=\frac{219}{100}$
$=\frac{200+19}{100}$
$=\frac{200}{100}+\frac{19}{100}$
$=2+0.19$
$=2.19$

$\frac{-1}{2}=0.5$

$=3\frac{5}{1000}$
$=3+\frac{5}{1000}$
$=3+0.005$
$=3.005$

$0.000000375=375\times { 10 }^{ -9 }=\\3.75\times { 10 }^{ -7 }=\cfrac { 375 }{ 100 } \times { 10 }^{ -7 }$
$=\cfrac { 15 }{ 4 } \times { 10 }^{ -7 }=3\cfrac { 3 }{ 4 } \times { 10 }^{ -7 }$

$4\frac{7}{8}=\frac{39}{8}=4.875$

$\frac{4}{10}+\frac{2}{1000}= 0.4+0.002=0.402$

$0.004=\frac{0.004}{1}$
Here, we have three numbers after decimal point.
So, we multiply by both numerator and denominator by $1000.$
$=\frac{0.004\times1000}{1\times1000}$
$=\frac{4}{1000}$
$\therefore$ Fraction for 0.004 is $\frac{4}{1000}$

We know that $1000m = 1km.$
Therefore, $1\text{m}=\frac{1}{1000}\text{m}=0.001\text{km.}$

In $16.534$, place value of $3$
$= 3$ hundredths $= 0.03$
$=\frac{3}{100}$

$\frac{4}{100}+\frac{7}{10000}$
$= 0.04 + 0.0007$
Converting into like decimals:
$0.0400 + 0.0007 = 0.0407$

We know that $1000g = 1kg.$
Therefore, $1\text{g}=\frac{1}{1000}\text{kg}=0.001\text{kg}$
$5\text{g}=\frac{5}{1000}\text{kg}=0.005\text{kg}$
Therefore, $2kg 5gm$
$= 2kg + 0.005kg$
$= 2.005kg$

Let $3889 + 12.952 - x = 3854.002$
Then $x = (3889 + 12.952) - 3854.002$
$= 3901.952 - 3854.002$
$= 47.95$

$\frac{5}{100}=.05$

$4\frac{3}{1000}=4.03$

$5.5 - 4.17 = 1.33$

We know that $1000ml = 1$ litre.
Therefore, $1\text{ml}=\frac{1}{1000}=0.001\text{ litre}$
$15\text{ml}=\frac{15}{1000}=0.015\text{ litre}$
So, $15$ litre and $15ml$
$= 15$ litre $+ 0.015$ litre
$= 15.015$ litres.

$25.369$
In this, $5$ lies on ones place.
$\therefore$ Place value of $5 = 5 \times 1 = 5$

$\frac{3}{10}$ is equal to $0.3$. Since the denominator is $10$, we have to mark the decimal such that $3$ is in the tenth place.

$\because 6.3 - 2.8 = 3.5$

To find the percent of a given number, we will multiply it with $100$
Let the number in decimal be $x$
When converted to percent, the number becomes $x \times 100 = 0.002$
Which gives $x = 0.00002$

$10\frac{2}{10}\Rightarrow10\frac{2}{10}=\frac{102}{10}=10.2$

$2.1 = 2.100 and 2.005$
$2.100 > 2.055$
$\Rightarrow 2.1 > 2.055$

The sum of $11.006 + 34 + 0.72$ is $45.726$
Now, the number $45.726$ is rounded off as $45.73.$
Again it is rounded to nearest tenths as $45.7.$

Let $x = 1.263263263$ [we multiply it by $1000]$
Here $3$ digits are repeated
$1000x = 1263.263263....$
$x = 1.263263...$
$999x = 1262$
$\Rightarrow\text{x}=\frac{1262}{999}$
The recurring decimal $1.263$ in a fraction form is equal to $\frac{1262}{999}$

Given decimal number is $15.526$
In this, $2$ lies on one-hundredth place.
$\therefore$ Place value of $2= \frac{2}{100} = 0.02$

$\frac{3}{100}+\frac{5}{10000}$
$=0.03+0.0005$
$=0.0305$

$\frac{134}{1000}=0.134$

The whole parts of all the above numbers are equal. Comparing the tenth parts, we see that two of the decimals have a tenth part $0$ and two have a tenth part $3$. Leaving aside the decimals that have a tenth part $0$, we have $2.3$ and $2.33$. Comparing them, we find that $2.33$ is greater than $2.3$, because, in $2.3$, there is no hundredth part, but in $2.33$, the hundredth part is $3.$

$3.\overline{87}-2.\overline{59}= (3+0.\overline{87})-(2+0.\overline{59})$
$=\Big(3+\frac{87}{99}\Big)-\Big(2+\frac{59}{99}\Big)$
$=1+\Big(\frac{87}{99}-\frac{59}{99}\Big)$
$=1+\frac{28}{99}$
$=1.\overline{28}$

We need to find value of $0.0001289 - 0.0000000274 \times 1293 + 0.0000419032$
We have, $0.0001288726 \times 1293.0000419032$
$= 0.166632277$

Decimal means divide the numerator by the denominator.
Here, Numerator $= 4999$ and Denominator
$=1000\Rightarrow\frac{4999}{1000}=4.999$

The conversion formula for celcius to farenheit is $=\Big(\text{C}\times\frac{9}{5}\Big)+32$

$256.36, 256.56, 256.26, 256.46$
As integral part of all the numbers is same $(256),$ we compare them by fractional part, greater the fractional
part, greater is the number.
In ascending order, $256.26, 256.36, 256.46, 256.56$

$\frac{9}{1000}=0.009$

Total expenditure $= Rs.((2 \times 52.98) + (3 \times 12.98) + (2 \times 300.5))$
$= Rs.(105.96 + 38.94 + 600.10) = Rs. 745$
Amount of money left with her $= Rs. (5000 - 745) = Rs. 4255$

The fraction $\frac{7}{100}$ in decimal form is $0.07.$

$\frac{3}{25}=0.12$
$\begin{aligned}
& \text { 25) } 30(0.12 \\
& \frac{-25}{50} \\
& \frac{-50}{0} \\
& \hline
\end{aligned}$

Let ? be $\text{x}8.8=6+\frac{7}{\text{x}}$
$8.8-6=\frac{7}{\text{x}}$
$\frac{7}{\text{x}}=2.8$
$\frac{7}{2.8}=\text{x}$
$\text{x}=\frac{5}{2}$
$\text{x}=2$

Place Value Definition:
It is the value of the digit with reference to its position in the number. For example, $238$ has $2$ hundred, $3$ tens and $8$ ones.
Therefore ans is $90,00,000$

$\because 1.1 - 0.3$
$= 0.8$

$2\frac{17}{100}=2.17$

Requried number $= 301.01 - 0.101 - 198.01$
$= 301.01 - 198.111 = 102.899$

$417.25 - 41.72 - 4.53$
$= 371.$

Since $1m = 100\ cm$
$\therefore150\text{cm}=\frac{150}{100}=1.5\text{cm}$

$\because 5.01 - 3.6$
$= 5.01 - 3.60 = 1.41$

$\underline{\ \ \ \ 0.350\\-0.035}\\\underline{=0.315}$

$\frac{6}{1000}$
$= 6$ thousandths $= 0.006$

$2kg 56g = 2.056kg$
($\because$ $1000g = 1kg)$

$5.5, 6.6, 7.7, 8.8$ are like decimals, since the number of decimals is the same.

$2\frac{1}{25}$
$=2+\frac{1}{25}\times\frac{1}{4}$
$=2+\frac{4}{100}$
$=2.04$

$1.5625 + 0.75 - 0.3125$
$= 2.3125 - 0.3125 = 2$

$31.08=31+0.08$
$=31+\frac{8}{100}$
$=31+\frac{\frac{8}{4}}{\frac{100}{4}}$
$=31+\frac{2}{25}$
$=31\frac{2}{25}$

$\frac{3}{25}=\frac{3\times4}{25\times4}=\frac{12}{100}=0.12$

$\frac{6}{25}$
$\frac{6\times4}{25\times4}$
$\frac{24}{100}$
$=0.24$

 $24.8=24\frac{8}{10}$
$24\frac{4}{5}$

$1$ paisa $= 0.01 Rs$
$\Rightarrow 50$ paise $= 0.50$
$Rs. 47$ and $50$ paise can hence be written as $Rs. 47.50$

$1$ meter $= 100\ cm$
So, $88\text{cm}=\frac{88}{100}\text{ metar}$
$= 0.88 \text{ meter}$

$4+\frac{3}{100}=\frac{400+3}{100}=4.03$

The smallest possible decimal fraction upto three decimal places $=\frac{1}{1000}=.001$

Given $\frac{3}{13}$ If we divide $3$ by $13$ we get $0.230769$ which is repeating and non-terminating.

Weight of rice $= 4\ kg \ 500g = 4.500\ kg$
Weight of sugar $= 5\ kg \ 650g = 5.650\ kg$
Weight of atta $= 12\ kg \ 600g = 12.600\ kg$
$\therefore$ Total weight of all items $= (4.500 + 5.650 + 12.600)\ kg$
$= 22.750\ kg.$

$\because 2 - 0.7$
$= 2.0 - 0.7 = 1.3$

The given numbers are $0.4,15.46$ and $0.002$
$\Rightarrow 15.46 + 0.4 + 0.002 = 15.46 + (0.4 + 0.002)$
$= 15.46 + 0.402$
$= 15.862$
$\therefore$ Sum of $0.4,15.46$ and $0.002$ is $15.862$

$2+\frac{3}{10}+\frac{4}{100}$
$=2+\frac{30}{100}+\frac{4}{100}$
$=2.34$

$\frac{7}{10}=0.7$