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Question Video: Comparing Decimal Numbers with Fractions Mathematics

Is 0.89 less than, greater than, or equal to 6 out of 7?


Video Transcript

Is zero and eighty-nine hundredths less than, greater than, or equal to six out of seven?

We’re trying to compare zero and eighty-nine hundredths to six out of seven. A better way to write that would be in its fraction form, six over seven. But we’re still not really ready to compare eighty-nine hundredths and six over seven. We don’t wanna compare this decimal to a fraction.

Instead, we want to take six-sevenths and find its decimal form. We do that with division. First, we recognise that seven goes into six zero times. We’ll need to add a decimal and then a zero. From there we can ask how many times does seven go into 60. Seven can be divided into 60 eight times. Eight times seven equals 56. And then we subtract 56 from 60, which equals four.

We’re not ready to compare these two yet, so we add another zero, bring that zero down, and ask how many times does seven go into 40. Seven goes into 40 five times. Five times seven equals 35. Subtract 35 from 40, and you have five. We’re going to add one more zero, and I’ll show you why.

Bring down that zero. How many times does seven go into 50? Seven goes into 50 seven times. Seven times seven equals 49. 50 minus 49 equals one. We could go on and on and on, adding zero after zero because seven does not divide into six evenly. But our goal is to compare six-sevenths to eighty-nine hundredths, and we can round this quotient to help us do that.

Because eighty-nine hundredths is in the hundredths place, we want to round our decimal here to the hundredths place. In our quotient, there was a five in the hundredths place and a seven in the thousandths place. That seven tells us we need to round up.

Six divided by seven rounded to the nearest hundredths place would be equal to eighty-six hundredths. Now we have a decimal to compare to a rounded decimal. Eighty-nine hundredths is greater than eighty-six hundredths. And that means eighty-nine hundredths is greater than six-sevenths.

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