Comparing and ordering decimals

Which is greater, zero point nine or zero point eight six? Try it first. Pause if you like. Does having more digits after the decimal point make a number greater? Compare matching places to find out. The digits in the ones place of both numbers are the same. Each number has zero ones. Write zero point nine as zero point nine zero. It has the same value. Compare hundredths. Compare the digits in the tenths place. Both rows use the same place, immediately after the decimal point. Nine is greater than eight. The tenths are the first unequal digits, so they decide the comparison. So zero point nine zero is greater than zero point eight six. The greater number is zero point nine. Stop at the first unequal place. The six in the hundredths cannot overturn the comparison at the tenths.

In the decimal five point blank two four, the digit in the tenths place is hidden. The decimal is smaller than five point three two four. What is the greatest digit that can go in the hidden place? Try it first. Pause if you like. Smaller than is a strict comparison. Would placing a three in the hidden cell give a smaller number, or an equal number? The digits in the ones place of both numbers are the same. Both have five ones. Compare the digits in the tenths place. That is the hidden place. Five point three two four has three in the tenths place. A three in the hidden cell would make both decimals equal. Their hundredths and thousandths also match, so three does not work. The hidden digit must be smaller than three. The greatest possible digit is two. Five point two two four is smaller than five point three two four. Start at the greatest place. The first unequal digit decides.