Rounding decimals

Round three point eight nine five to two decimal places. Try it first. Pause if you like. We keep two decimal places. Which digit just beyond them decides? The digit in the thousandths place is five. It decides what happens to the hundredths. Five and greater than five rounds up, so add one to the digit in the hundredths place. Nine hundredths plus one hundredth make ten hundredths. Rename ten hundredths as one tenth. Add that tenth to the eight tenths. Eight tenths plus one tenth is nine tenths. There are zero hundredths left to write. Three point eight nine five is three point nine zero, to two decimal places. Keep the zero. It shows that the answer is written to two decimal places. The last written place is the hundredths. Read the next digit. Five and greater than five rounds up. Then write exactly the number of decimal places requested.

A decimal with three decimal places is rounded to six point four zero at two decimal places. Find the smallest possible decimal and the greatest possible decimal. Try it first. Pause if you like. Work backwards. Where does rounding up to six point four zero start? Where does it stop? Use the place-value table. The thousandths digit decides the rounding. Start with six point three nine five. Its thousandths digit is five, so it rounds up to six point four zero. Six point three nine five is the smallest possible decimal. One thousandth smaller would be six point three nine four. Its deciding digit is four, so it would round to six point three nine. Now consider six point four zero four. Its thousandths digit is four, so it rounds down to six point four zero. Six point four zero five would round up to six point four one. It is the first value outside the upper end. This upper boundary still rounds to six point four zero. Six point four zero four is the greatest possible decimal. From six point three nine five through six point four zero four, every three-place decimal rounds to six point four zero. The next digit decides the rounding. For a range, check both ends and the value just outside each end.