User:MathMan64~enwikibooks/Arithmetic/Rounding

= Rounding =

Rounding rules
The most commonly used method of rounding numbers is:
 * less than five, round down,
 * five or more, round up.

To round down, change the appropriate digits on the right to zeros. Changing a digit to a zero makes the number smaller, rounds it down.
 * Changing 72 to 70 yields a smaller number.

To round up, add one to the appropriate digit, and then change the digits on the right to zeros. Adding 1 makes the number larger, rounds it up.


 * Changing 47 to 50 yields a larger number.

If any of these zeros are on the right of the decimal point, they are not written.
 * Rounding 3.7238 could change it to 3.724

To place value
Many times rounding is done to a stated place value. This is accomplished by;
 * finding the appropriate place,
 * looking one place to the right and deciding whether or not to add one,
 * changing all the digits to the right to zeros and deciding whether to write the zeros.

Whole numbers
Round 47,268 to the hundreds place.
 * Find the 2 in the hundreds place.
 * Look at the 6. It is 5 or larger.  Thus add 1 to the 2.
 * Write the digits to the left with no change, those to the right as zeros.
 * 47,268 rounded to the hundreds place is 47,300

Round 41,579,243 to the ten millions place.
 * Find the 4 in the ten millions place.
 * Look at the 1. It is smaller than 5.  Thus do not add 1 to the 4.
 * Write the digits to the left with no change, those to the right as zeros.
 * 41,579,243 rounded to the ten millions place is 40,000,000

Decimals
Round 7.3158 to the hundredths place.
 * Find the 1 in the hundredths place.
 * Look at the 5. It is 5 or larger.  Thus add 1 to the 1.
 * Write the digits to the left with no change, those to the right are not written.
 * 7.3158 rounded to the hundredths place is 7.32

Round 0.003961 to the ten thousandths place.
 * Find the 9 in the ten thousandths place.
 * Look at the 6. It is 5 or larger.  Thus add 1 to the 9.  But 9 + 1 is 10.  Think 39 + 1 is 40.  This zero is needed because it is in the place that was rounded to.
 * The 6 and 1 are changed to zero but not written.
 * 0.003961 to the ten thousandths place is 0.0040

To significance
Sometimes rounding is done to a number of significant digits. Significant digits are those that are not zeros, and the zeros that have non-zero digits on both sides.
 * 230,000 has 2 significant digits (2 and 3.)
 * 0.00592 has 3 significant digits (5, 9 and 2.)
 * 3.142 has 4 significant digits (3, 1, 4 and 2.)
 * 50,900 has 3 significant digits. The zero in the thousands place has non-zero digits on both sides.
 * 0.00420086 has 6 significant digits. The zeros in the hundred thousandths and millionths places have non-zero digits both to the left and to the right.

When rounding to a stated number of significant digits, the most significant digits are used. These are the significant digits that are the farthest to the left.

Round 432,749 to 2 significant digits.
 * The 4 and 3 are the most significant digits.
 * Look at the 2. It is small.  Do not add.
 * Change the digits to the right to zeros.
 * 432,749 rounded to 2 significant digits is 430,000.

Round 68.251 to 3 significant digits.
 * The 6, 8 and 2 are the most significant digits.
 * Look at the 5. It is large.  Add 1 onto 2.
 * Do not write the digits to the right.
 * 68.251 rounded to 3 significant digits is 68.3

Round 0.008627 to 1 significant digit.
 * The 8 is the most significant digit.
 * Look at the 6. It is small.  Add 1 onto 8.
 * Do not write the digits to the right.
 * 0.008327 rounded to 1 significant digit is 0.009