explain why thirteen hundredths are equivalent to one hundred thirty thousandths?

Answer 1

thirteen hundredths=13/100
one hundred thirty thousandths=130/1000
cancelling by 10 this is =13/100
hence the question

Answer 2

You can explain this in terms of decimals and fractions.

"Thirteen hundredths" as a decimal = 0.13
Note that after a decimal point, the first digit to the right is the tenths place, and the next is the hundredths. This is not the same as tens and hundreds to the left of the decimal point.

"One hundred thirty thousandths" as a decimal = 0.130
If you have a 0 after a decimal point following non-zero numbers, they don't matter. You can have 0.130000000000 and it will still always equal 0.13. (Note, however, that in a decimal like 0.00013, the zeros DO matter.)

In terms of fractions, look at it this way:
13/100 = thirteen hundredths, or 13 over 100.
130/1000 = one hundred and thirty thousandths, or 130 over 1000.

If you multiplied the top fraction, 13/100, by one, you would have an equivalent fraction.

13/100 x 1 = 13/100, right?
Now, remember that 10/10 = 1. Any fraction consisting of a number over itself is 1.
So you can also say that
13/100 x 10/10 = 130/1000.

Therefore, 13/100 = 130/1000!

Answer 3

Because 13 hundredths is equivalent to " 13 / 100 " (thirteen divided by 100). 130 thousandths is equivalent to " 130 / 1000 " which is the same as saying " ( 13 / 100 ) * ( 10 / 10 ) ." "10 / 10" of course is 1.