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express the missing divisor using a power of 10. Explain your reasoning using a place value model.

a. 5.2 ÷ ___ =0.052    b. 7,650÷__ =7.65

Sagot :

a:  5.2 / 100 = .052  the reason for this is the 5 goes from the ones place to the hundredths place
b:  7,650 / 1000 = .7.65 this is because the decimal jumps 3 spots to the left

Answer:

[tex]a) 10^{2}\\b)~ 10^{3}[/tex]

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:

[tex]x^{-a} = \displaystyle\frac{1}{x^a}\\\\10^{-2} = \frac{1}{10^2} = \frac{1}{100}[/tex]

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:

[tex]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[/tex]

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