Question

The following equations involve different quantities and use different operations, yet produce the same result. Use a place value chart and words to explain why this is true.

Answer 1

Because 10 squared is 10×10 which is 100 so 413,000÷10×10=4130

Answer 2

Answer with Step-by-step explanation:

We are given that two expression in which different operations are used.

$4.13\times 10^3=4130$

and $413000\div 10^2=4130$

We are given that using different operation and quantities yet produce same result.

We have to explain why this is true using pl;ace value chart.

Place value of 4 in 4.13=4

Place value of 1 in 4.13=$\frac{1}{10}$

place value of 3 in 4.13=$\frac{1}{100}$

Place value of 4 in 413000=400000

Place value of 1 in 413000=10000

Place value of 3 in 413000=3000

$4.13=4+1\times 10^{-1}+3\times 10^{-2}$

$413000=4\times 10^5+1\times 10^4+3\times 10^3$

$(4+1\times 10^{-1}+3\times 10^{-2})\times 10^3=4000+100+30=4130$

$(4\times 10^5+1\times 10^4+3\times 10^3)\div 10^2=4000+100+30=4130$

$10^3=1000$

$10^2=100$

When we remove decimal point in 4.13 then we write 100 in denominator and multiply with 1000 then the 100 in denominator cancel out with two zeroes of 1000.Then 10 remain in multiply then  multiply 10 with 413 and get 4130.

When 413000 divided by 100 then two zeroes of 100  cancel out with two zeroes of 413000 and then  4130 remain.

Therefore, both results true.