Rounding

Once you have performed a calcuation and determined the correct number of significant digits to keep, you must round off your answer. There are two steps involved in rounding off a number, and you are already likely to be familiar with the rounding process from your earlier math classes. The steps for rouding are:

Starting from the leftmost significant digit, move to the right until you have as many digits as you are allowed to keep. Then look to the immediate right and note the number present.

If the number to the right is a 5, 6, 7, 8, or 9, round the last significant digit up one. If the number to the right is a 4, 3, 2, 1, or 0, keep the last significant digit the same.

Examples:

Round 1034.56 to 4 significant digits.

Step 1: Start with 1 and keep 0, 3, and 4. To the immediate right of 4 is a 5.

Step 2: From the above rules, since we have a 5 to the immediate right, we round 4 up to 5. ANSWER: 1035

Round 0.000343 to 1 significant digit.

Step 1: Start from the left and skip all of the 0's (they aren't significant). The first significant digit encountered is a 3. To the immediate right of the 3 is a 4.

Step 2: From the rules above, since we have a 4 to the immediate right, we leave the 3 alone. ANSWER: 0.0003

Round 4589 to 3 significant digits.

Step 1: Start from the 4 at the left and keep the 5 and 8. To the immediate right of the 9 is another 9.

Step 2: From the rules above, since we have a 9, we must round up. ANSWER: 4590

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