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Exponents and Powers — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSExponents and Powers5 Marks
Question
Express the given information in Scientific notation (standard form) and then arrange them in ascending order of their size.
  Deserts of the world Area (in sq km)
$1$ Kalahari, South Africa $932,400$
$2$ Thar, India $199,430$
$3$ Gibson, Australia $155,400$
$4$ Great Victoria, Australia $647,500$
$5$ Sahara, North Africa $8,598,800$
✓

Answer

1. Area of Kalahari, South Africa $=932,400$
$=932400.00\left[\therefore \text { standard form a } \times 10^{k}\right]$
$=9324 \times 10^2$
$=9.324 \times 10^3 \times 10^2$
$=9.324 \times 10^6$
2. Area of Thar, India $=199,430$
$=199430.00$
$=19943 \times 10^1$
$=1.9943 \times 10^4 \times 10^1$
$=1.9943 \times 10^5$
3. Area of Gibson, Australia $=155,400$
$=155400.00$
$=1554 \times 10^2$
$=1.554 \times 10^3 \times 10^2$
$=1.554 \times 10^5$
4. Area of Great Victoria, Australia $=647,500$
$=647500.00$$=6475 \times 10^2$
$=6.475 \times 10^3 \times 10^5$
$=6475 \times 10^5$
5. Area of Sahara, North-Africa $=8,598,800$
$=8598800.00$
$=85988 \times 10^2$
$=8.5988 \times 10^4 \times 10^2$
$=85988 \times 10^6$
Two numbers written in scientific notation can be compared.
The number with the larger power of $10$ is greater than the number with the smaller power of $10$.
If the powers of ten are the same, then the number with larger factor is the larger number.
Hence, required ascending order of the size will be
Gibson, Australia < Thar, India < Great Victoria, Australia < Kalahari, South Africa < Sahara, North-Africa.

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