Answer:
\(a) 10^{2}\\b)~ 10^{3}\)
Step-by-step explanation:
We are given the following information.
We have to complete the division problem by filling in the right powers of 10.
We know that:
Negative exponential powers:
Any number raised to negative power can be written as:
\(x^{-a} = \displaystyle\frac{1}{x^a}\\\\10^{-2} = \frac{1}{10^2} = \frac{1}{100}\)
Division by powers of 10:
- Move the decimal point to the left as many places as there are zeros in the factor we are dividing the number.
- Move the decimal point one step to the left when dividing by 10.
- Move the decimal point two steps to the left when dividing by 100 and so on.
Solving can be done in the following manner:
\(a)~5.2 \div 10^{2} = 0.052\\\\= 5.2\times \displaystyle\frac{1}{100} = \frac{5.2}{100} = 0.052\\\\b)~7650 \div 10^{3} = 7.650\\\\= 7650\times \displaystyle\frac{1}{1000} = \frac{7650}{1000} = 7.65\)
