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Learning Objectives. Give an example of a measurement whose number of significant digits is clearly too great, and explain why. State the purpose of rounding off, and describe the information that must be known to do it properly. Round off a number to a specified number of significant digits.
- 1.9: Rounding Off Numbers
Before dealing with the specifics of the rules for...
- 1.9: Rounding Off Numbers
When you round off, you change the value of the number, except if you round off a zero. Following the old rules, you can round a number down in value four times (rounding with one, two, three, four) compared to rounding it upwards five times (five, six, seven, eight, nine).
Before dealing with the specifics of the rules for determining the significant figures in a calculated result, we need to be able to round numbers correctly. To round a number, first decide how many significant figures the number should have.
Rules Of Rounding Off Data. Rule # 1: If the digit to be dropped is greater than 5, then add "1" to the last digit to be retained and drop all digits farther to the right. For example: 3.67 7 is rounded off to 3.68 if we need three significant figures in measurement.
Rules for rounding off numbers. If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13. If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.
Rules for Rounding Numbers. If the first nonsignificant digit is less than 5, drop all nonsignificant digits. If the first nonsignificant digit is greater than or equal to 5, increase the last significant digit by 1 and drop all nonsignificant digits.
Rounding Your Final Answer. When you report your final calculated answer, you should write only the significant digits in the value – here is where you finally round off your value. For most numbers, the rules will be familiar:
