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Is zero and eighty-nine hundredths less than, greater than, or equal to six out of seven?
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We’re trying to compare zero and eighty-nine hundredths to six out of seven.
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A better way to write that would be in its fraction form, six over seven.
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But we’re still not really ready to compare eighty-nine hundredths and six over seven.
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We don’t wanna compare this decimal to a fraction.
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Instead, we want to take six-sevenths and find its decimal form.
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We do that with division.
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First, we recognise that seven goes into six zero times.
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We’ll need to add a decimal and then a zero.
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From there we can ask how many times does seven go into 60.
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Seven can be divided into 60 eight times.
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Eight times seven equals 56.
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And then we subtract 56 from 60, which equals four.
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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.
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Seven goes into 40 five times.
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Five times seven equals 35.
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Subtract 35 from 40, and you have five.
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We’re going to add one more zero, and I’ll show you why.
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Bring down that zero.
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How many times does seven go into 50?
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Seven goes into 50 seven times.
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Seven times seven equals 49.
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50 minus 49 equals one.
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We could go on and on and on, adding zero after zero because seven does not divide into six evenly.
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But our goal is to compare six-sevenths to eighty-nine hundredths, and we can round this quotient to help us do that.
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Because eighty-nine hundredths is in the hundredths place, we want to round our decimal here to the hundredths place.
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In our quotient, there was a five in the hundredths place and a seven in the thousandths place.
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That seven tells us we need to round up.
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Six divided by seven rounded to the nearest hundredths place would be equal to eighty-six hundredths.
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Now we have a decimal to compare to a rounded decimal.
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Eighty-nine hundredths is greater than eighty-six hundredths.
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And that means eighty-nine hundredths is greater than six-sevenths.