Question

Express the standard form: (i) radius of the earth= 6 400 000 m (ii) radius of hydrogen atom = 0.000 000 000 0529

Answer 1

i. 6.4 × 10⁶ m.

ii. 5.29 × 10⁻¹¹ m.

Step-by-step explanation:

To express a number in standard form, we write it in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer.

(i) radius of the earth= 6 400 000 m

To express the radius of the earth = 6 400 000 m in standard form, we count the number of decimal places after the first digit. We have 6 decimal places after digit 6. So, we put a decimal point between digit 6 and 4. So, we have 6.4. Since we have 6 decimal places after the six digit, the exponent of our base which is 10 is 6.

So, writing 6 400 000 in the form in a × 10ⁿ, we have a = 6.4 and n = 6. So, in standard form we have 6.4 × 10⁶ m.

So, 6 400 000 = 6.4 × 10⁶ m in standard form.

(ii) radius of hydrogen atom = 0.000 000 000 0529 m

To express the radius of hydrogen atom = 0.000 000 000 0529 m in standard form, we count the number of decimal places after the decimal point including the first non-zero digit. We have 11 decimal places after the decimal point up to and including the first non-zero digit which is digit 5. So, we put a decimal point after the first non-zero digit,5. So, we have 5.29. Since we have 11 decimal places after the decimal point, the exponent of our base which is 10 is -11. The exponent is negative since the digit places are taken after the decimal point.

So, writing 0.000 000 000 0529 m in the form in a × 10ⁿ, we have a = 5.29 and n = -11. So, in standard form we have 5.29 × 10⁻¹¹ m.

So, 0.000 000 000 0529 m = 5.29 × 10⁻¹¹ m in standard form.

Answer 2

I) 6.4 × 10^(6) m

II) 5.29 × 10^(-11) m

Step-by-step explanation:

Standard form is how we write very large number in such a way that it is easier to read.

Thus;

I) radius of the earth = 6 400 000 m

What we will now have is;

6.4 × 10^(6) m

II) radius of hydrogen atom = 0.000 000 000 0529 m

What we will have is;

5.29 × 10^(-11) m