Rounding

Rounding is a process used to reduce the number of digits in a number while keeping its value close to what it was.

Rounding can be done to:

1. Decimal places or
2. Significant figures.

Rounding to Decimal Places

Decimal places refer to the number of digits to the right of the decimal point in a number.

To round to a specific number of decimal places, follow these steps:

3. Identify the digit at the place you are rounding to.
4. Look at the next digit (the one immediately after the place you are rounding to).

• If this digit is 5 or more, round up the identified digit.
• If this digit is 4 or less, round down the identified digit.

5. Remove all the digits after the place you are rounding to.

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Rounding to Significant Figures

Significant figures are the digits that carry meaning contributing to the number's precision.

To round to a specific number of significant figures, follow these steps:

3. Identify the digit at the place of the last significant figure you need.
4. Look at the next digit (the one immediately after the last significant figure).

• If this digit is 5 or more, round up the identified digit.
• If this digit is 4 or less, round down the identified digit.

5. Replace all digits after the last significant figure with zeros (if rounding whole numbers) or remove them (if rounding decimals).

Rounding to significant figures can be tricky, especially when dealing with numbers that include zeros. Understanding which digits count as significant figures is important.

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Which Digits Are Significant?

1. Non-zero digits (1-9):

• Always significant. These digits are important no matter where they appear in the number.
• Example: In 345, all three digits (3, 4, and 5) are significant.

2. Zeros between non-zero digits:

• Always significant. These zeros are sandwiched between other significant digits and matter for precision.
• Example: In 305, the zero is significant because it is between 3 and 5. So, all three digits (3, 0, and 5) are significant.

3. Zeros after a decimal point and after a non-zero digit:

• Significant. These zeros are important because they show precision in a measurement.
• Example: In 0.450, the digits 4, 5, and the zero after 5 are significant. So, all three digits (4, 5, and 0) count.

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Which Digits Are Not Significant?

1. Zeros before the first non-zero digit (in decimals):

• Not significant. These zeros are just placeholders to show where the decimal point is.
• Example: In 0.0034, the first three zeros just help position the decimal point and are not significant. The significant figures here are 3 and 4.

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Recap

• Count all non-zero digits (1-9) as significant.
• Count zeros between non-zero digits or after a non-zero digit in a decimal number as significant.
• Ignore zeros that come before the first non-zero digit in a decimal number (they're just placeholders).