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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.
- 4.6: Significant Figures and Rounding
State the purpose of rounding off, and describe the...
- 4.6: Significant Figures and Rounding
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. Explain how to round off a number whose second-most-significant digit is 9.
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).
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 counting significant figures are summarized below. Zeros within a number are always significant. Both 4308 and 40.05 contain four significant figures. Zeros that do nothing but set the decimal point are not significant. Thus, 470,000 has two significant figures.
Rounding Rules. Identify the first digit to be dropped (immediately to the right of the last significant figure). If it is: less than 5 (0, 1, 2, 3, or 4), then leave the last significant figure unchanged (round down) example: rounding 52.51 to three significant figures becomes 52.5.
1 wrz 2014 · 1) Do the subtraction, but keep the *exact* number while noting that the rounded number was supposed to have 2 sig figs. (1.178 1.03) (1.178 1.03) 2) Do the division with the exact number and the denominator, and since this step produces the final result, NOW you round, rounding to 2 sig figs per the note in Step 1.
