Move the decimal to the left until it passes the first non-zero integer.The steps to converting numbers to scientific notation using decimals are: When you have a large number, you use decimals and exponents to show it as a power of ten. Because the numbers to the right of a decimal point are parts of the next number, rounding up provides some of the missing pieces to that number.ĭecimals operate within scientific notation to express very large or very small numbers in mathematical shorthand. The rounding rule applies whether you round to four decimal places (the nearest one-thousandth), five decimal places (the nearest ten-thousandth), six decimal places (the nearest hundred-thousandth), or lower. 0.55 3 rounds down to 0.55 (3 thousandths rounds down to zero hundredths, and 0.55 + 0.00 = 0.55).2.87 1 rounds down to 2.87 (1 thousandth rounds down to zero hundredths, and 2.87 + 0.00 = 2.87).If you round to three decimal places (or round to the nearest one hundredth), it looks like this: 0.5 5 rounds up to 0.6 (5 hundredths rounds up to 1 tenth, and 0.5 + 0.1 = 0.6).2.8 7 rounds up to 2.9 (7 hundredths rounds up to 1 tenth, and 2.8 + 0.1 = 2.9).The same goes when you round to two decimal places, or round to the nearest tenth. 4 rounds down to 100 (the 4 tenths rounds down to 0, and 100 + 0 = 100) 5 rounds up to 1 (the 5 tenths rounds up to 1, and 0 + 1 = 1) 2 rounds down to 89 (the 2 tenths rounds down to 0, and 89 + 0 = 89) 9 rounds up to 3 (the 9 tenths rounds up to 1, and 2 + 1 = 3) If it's 5 or higher, the digit on its left goes up by one digit (rounds up).įor example, if you round up to one decimal place or the nearest one:
If the digit you're looking at is a 1, 2, 3, or 4, the digit on its left stays the same (rounds down). The process of rounding with decimals is the same as rounding with whole numbers. It can also help you identify whether a number is very large or very small, depending on the placement of the decimal. Understanding how the decimal impacts the size of the number can help you conceptualize multiplication much more easily. If you move the decimal point to the left, you're making the number smaller by a power of ten.
Moving the decimal point to the right can make the number larger by a power of ten.
You may already be familiar with place value in larger numbers, but it works the same way in very small numbers as well.įor example, in the number 1.23456, the place value looks like this: Decimal place value refers to the place value of numbers smaller than one.
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