The exponent shows the size

The idea

In scientific form the exponent is the most important part: it indicates the number of digits, and increasing it by 1 makes the number 10 times larger, far more than any change in the coefficient.

2 crore people in Mumbai

The population of Mumbai is about 2 crore. In scientific form: 2 × 10^7.

Which change makes the population bigger: changing the 2 to 3, or changing the 7 to 8?

• The 2 to 3
• The 7 to 8
• Both change it the same

Change the 2, then the 7

Press + on the coefficient once. Then press + on the exponent once. Watch the before and now bars.

The exponent is the star

In scientific form the exponent is the most important part: it indicates the number of digits, and increasing it by 1 makes the number 10 times larger, far more than any change in the coefficient.

2 × 10^7 → 3 × 10^7: 2 crore → 3 crore, one-half more. 2 × 10^7 → 2 × 10^8: 2 crore → 20 crore, 10 times as much.

Notes

In scientific form the exponent shows the size: it tells the number of digits, and +1 makes the number 10 times larger.

Check yourself

Which change makes 4 × 10^5 larger by the most?

How many times larger is 3 × 10^9 than 3 × 10^8?

Answer: 10

3 × 10^9 = 3 × 10 × 10^8 = 30 × 10^8, which is 10 times 3 × 10^8.

How many digits does 6 × 10^8 have?

Answer: 9

6 × 10^8 = 6,00,000,000: the digit 6 and 8 zeros, so 9 digits. (The number of digits is the exponent + 1.)

Which is bigger: 9 × 10^6 or 1 × 10^7?

• 4 → 5: it becomes 5 × 10^5. That makes it 1.25 times as large.
• 5 → 6 in the exponent: it becomes 4 × 10^6 — correct. Yes! Raising the exponent by 1 makes it 10 times as large.
• 4 → 9: it becomes 9 × 10^5. That makes it a bit more than 2 times as large. Raising the exponent by 1 gives 10 times.
• 9 × 10^6. 9 is bigger than 1, but the exponent decides. 9 × 10^6 = 90,00,000, only 90 lakh.
• 1 × 10^7 — correct. Yes! 1 × 10^7 = 1,00,00,000 (1 crore), which is more than 90 lakh.
• They are equal. 9 × 10^6 = 90 lakh and 1 × 10^7 = 1 crore. They are not equal.