Question

Round off or add zeros to each of the following to give an answer with three significant figures: a. \(5080 \mathrm{~L}\) b. \(37400 \mathrm{~g}\) c. \(104720 \mathrm{~m}\) d. \(0.00025082 \mathrm{~s}\)

Short answer

a. 5080 Lb. 37400 gc. 105000 md. 0.000251 s

Step-by-step solution

Identify the Number of Significant Figures

For each value given, observe the digits and identify how many significant figures it currently has.

Round Off to Three Significant Figures

If the number currently has more than three significant figures, round the value such that only the first three significant figures remain, adjusting the value accordingly.

Add Zeros if Insufficient Significant Figures

If the number has fewer than three significant figures, add zeros as required to ensure there are exactly three significant figures.

Apply Steps to Each Value

a. For 5080 L, the first three significant figures are 5, 0, and 8. The fourth digit is a zero, so no change is needed. Final value: 5080 L.b. For 37400 g, the first three significant figures are 3, 7, and 4. Final value after rounding off: 37400 g.c. For 104720 m, the first three significant figures are 1, 0, and 4. The fourth digit is 7, rounding up the third digit from 4 to 5. Final value: 105000 m.d. For 0.00025082 s, the first three significant figures are 2, 5, and 0. The fourth digit is 8, rounding up the third digit from 0 to 1. Final value: 0.000251 s.

Key concepts

rounding numbers

Rounding numbers is an essential skill in math and science. It simplifies numbers, making them easier to work with without significantly changing their value. To round a number, you usually look at the digit right after the one you want to keep. If that digit is 5 or higher, you round up the last digit you keep. If it's less than 5, you round down. For instance, when rounding 37424 to three significant figures, you look at the digit after the third significant figure (2 in this case). Since 2 is less than 5, you round down, keeping 37400 as the rounded number.

significant figures identification

Identifying significant figures is critical for ensuring the precision of measurements. Significant figures include all the non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal portion. For example, in the number 5080, the significant figures are 5, 0, and 8—three significant figures. Leading zeros are never considered significant figures. In the number 0.00025082, the significant figures are 2, 5, and 0. Even though there are many zeros, only three digits count as significant figures.

significant figures rules

There are a few basic rules for dealing with significant figures:

• All non-zero numbers are always significant.
• Any zeros between significant figures are significant.
• Trailing zeros in a decimal number are significant.
• Leading zeros are not significant.

Understanding these rules helps you determine the exact number of significant figures in any given number. For example, the number 104720 has five significant figures, but when rounding to three, it becomes 105000, as the digit to the fourth place is 7 (which rounds the third place up from 4 to 5).

adding zeros for precision

Sometimes, you need to add zeros to maintain a number's precision. This usually happens when a number has fewer significant figures than required. For example, if you need to round 0.004 to three significant figures, it becomes 0.00400. You added two trailing zeros to ensure there are exactly three significant figures. Likewise, 508 becomes 5080, since adding a zero changes it to three significant figures. Be careful with where you place zeros—they can change the value if not placed correctly.