Question

- Write each expression as a multiple of a power of 10:
a. 0.04
b. 0.072
c. 0.0000325
d. Three thousandths
e. 23 hundredths
f. 729 thousandths
g. 41 millionths

Answer 1

Answer:

To write the following expressions as a multiple of a power of 10 you need to take each of the numbers and raise them to the power of 10.

An easy way to do this is to find the decimal point and move it over one spot to the right.

a. 0.04- move the decimal one to the right and you get that 0.04^10=00.4.

b. 0.072-move the decimal to the right one spot you get 0.072^10=00.72.

c. 0.0000325-move your decical to get 0.0000325^10=00.000325.

d. 0.003-move the decimal to get 0.003^10=00.03 or three hundredths.

e. 0.23-move your decimal to get 0.23^10=2.3 or two and three tenths.

f. 0.729-move you decimal to the right to get 0.729^10=07.29 or seven and twenty-nine hundredths.

g. 0.000041- move your decimal to the right to get 0.000041^10=00.00041 or forty-one hundred thousandths.

Hope this helps ;)

Answer 2

To write the expression as a multiple of a power of 10 ; we express the decimals in scientific notation :

0.04 :

• Two decimal points to the left ;

0.04 = $4 \times 10^{-2}$

0.072 :

• 3 decimal points to the left ;

0.072 = $7.2 \times 10^{-3}$

0.0000325 :

• Two decimal points to the left ;

0.04 = $3.25 \times 10^{-5}$

Three thousandth = 0.003 :

• 3 decimal places to the left

0.003 = $3 \times 10^{-3}$

23 hundredths = 0.023:

• 2 decimal places to the left

0.023 = $2.3 \times 10^{-2}$

729 thousandths = 0.00729 :

• 3 decimal places to the left

0.00729 = $7.29 \times 10^{-3}$

41 millionths = 0.0000041

• 6 decimal places to the left

0.0000041 = $4.1\times 10^{-6}$

Hence, the scientific representation.

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