Rounding means reducing the digits in a number while trying to keep its value similar. The result is less accurate, but easier to use.

Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

How to Round Numbers

• Decide which is the last digit to keep
• Leave it the same if the next digit is less than 5 (this is called rounding down)
• But increase it by 1 if the next digit is 5 or more (this is called rounding up)

Example: Round 74 to the nearest 10: We want to keep the "7" as it is in the 10s position. The next digit is "4" which is less than 5, so no change is needed to "7", so the answer will be 70 (74 gets "rounded down").

Example: Round 86 to the nearest 10: We want to keep the "8". The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9" so the answer will be 90 (86 gets "rounded up").

So: when the first digit removed is 5 or more, increase the last digit remaining by 1.

Rounding Decimals

First we need to know if we are rounding to tenths, or hundredths, etc. Or maybe to "so many decimal places". That tells us how much of the number will be left when we finish.

• 3,1416 rounded to hundredths is 3,14 as the next digit (1) is less than 5.
• 1,2635 rounded to tenths is 1,3 as the next digit (6) is 5 or more.
• 1,2635 rounded to 3 decimal places is 1,264 as the next digit (5) is 5 or more.

Rounding Whole Numbers

We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero.

• 134,9 rounded to tens is 130 as the next digit (4) is less than 5.
• 12.690 rounded to thousands is 13.000 as the next digit (6) is 5 or more.
• 15,239 rounded to units is 15 as the next digit (2) is less than 5.

Rounding to Significant Digits

To round to "so many" significant digits, count digits from left to right, and then round off from there.

Note: if there are leading zeros (such as 0,006), don't count them because they are only there to show how small the number is.

• 1,239 rounded to 3 significant digits is 1,24 as the next digit (9) is 5 or more.
• 134,9 rounded to 1 significant digit is 100 as the next digit (3) is less than 5.
• 0,0165 rounded to 2 significant digits is 0,017 as the next digit (5) is 5 or more.

Suppose we wanted to round off 838.274. Depending on which place value we're rounding to, the final result can vary.

• Round to the nearest hundred (838.274) is 800
• Round to the nearest ten (838.274) is 840
• Round to the nearest one (838.274) is 838
• Round to the nearest tenth (838.274) is 838.3
• Round to the nearest hundredth (838.274) is 838.27

Basic Rules of Rounding

When we "round to the nearest ________", regardless of what goes in that blank the steps are nearly always the same:

• Identify which place value we are rounding to. The smaller the place value, the more accurate the final result will be.
• Look to the next smallest place value, or simply put, the one directly to the right of the place value we're rounding to. For example, if we want to round to the nearest ten, we will look at the ones place.
• If this next smallest place value is less than five (0, 1, 2, 3, or 4), we leave the digit we want to round to alone. Any digits after that number (including the next smallest place value we just looked at) become zeros, or simply drop if after the decimal point. This is called rounding down.
• If the next smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), we increase the value of the digit we're rounding to by one. Just like before, any remaining digits before the decimal point become zeros, and any that are after the decimal point are dropped. This is called rounding up.

Examples

Round to the Nearest Hundred

3250

• Identify the hundreds digit: 3250
• Identify the next smallest place value (the digit to the right of the hundreds place): 3250
• Is that digit greater than or equal to five? YES - we round UP.
• The hundreds digit is increased by one, to 3. Every digit after it becomes a zero.

3250 rounded to the nearest hundred is 3300.

Round to the Nearest Ten

323.5

• Identify the tens digit: 323.5.
• Identify the next smallest place value (the digit to the right of the tens place): 323.5.
• Is that digit greater than or equal to five? NO - we round DOWN.
• The tens digit stays the same. Every digit after it becomes a zero. Digits after the decimal point are dropped.

323.5 rounded to the nearest ten is 320.

499

• Identify the tens digit: 499.
• Identify the next smallest place value (the digit to the right of the tens place): 499.
• Is that digit greater than or equal to five? YES - we round UP.
• The tens digit increases by one. Since 9+1=10, we carry over the 1 into the hundreds place. Each additional digit becomes a zero.

499 rounded to the nearest ten is 500.

Round to the Nearest Tenth

0.74

• Identify the tenths digit: 0.74.
• Identify the next smallest place value (the digit to the right of the tenths place): 0.74.
• Is that digit greater than or equal to five? NO - we round DOWN.
• The tenths digit stays the same. Since the remaining digits are all after the decimal point, they drop.

0.74 rounded to the nearest tenth is 0.7.

Round to the Nearest Hundredth

3.141

• Identify the hundredth digit: 3.141.
• Identify the next smallest place value (the digit to the right of the hundredths place): 3.141.
• Is that digit greater than or equal to five? NO - we round DOWN.
• The hundredths digit stays the same. Remaining digits after the decimal point are dropped.

3.141 rounded to the nearest hundredth is 3.14.

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