How To Find 2 Significant Figures

Learning Objective

Use cognition of significant figures to scientific calculations

Key Points

Significant figures are any not-zero digits or trapped zeros. They do not include leading or trailing zeros.
When going between decimal and scientific notation, maintain the same number of significant figures.
The final reply in a multiplication or division problem should comprise the same number of significant figures as the original number with the fewest significant figures.
In add-on and subtraction, the final reply should incorporate the aforementioned number of decimal places as the original number with the fewest number of decimal places.

Term

Significant FiguresThe digits that carry pregnant in a number and contribute to its precision.

Significant figures of a number are digits which contribute to the precision of that number. Numbers that do not contribute whatever precision and should not be counted as a significant number are:

leading or trailing zeros (those are place holders)
digits that are introduced past calculations that requite the number more precision than the original information allows.

PiThis calculator shows eight significant figures of pi.

Rules For Determining If a Number Is Significant or Not

All non-zero digits are considered significant. For example, 91 has two significant figures (9 and ane), while 123.45 has five pregnant figures (i, ii, 3, four, and v).
Zeros appearing between two not-zip digits (trapped zeros) are significant. Case: 101.12 has v significant figures: ane, 0, 1, 1, and 2.
Leading zeros (zeros before non-aught numbers) are not meaning. For example, 0.00052 has two pregnant figures: 5 and 2.
Trailing zeros (zeros after non-zilch numbers) in a number without a decimal are generally not significant (see below for more details). For example, 400 has merely one pregnant figure (4). The trailing zeros exercise non count as significant.
Abaft zeros in a number containing a decimal betoken are significant. For case, 12.2300 has six significant figures: ane, ii, 2, 3, 0, and 0. The number 0.000122300 still has only six significant figures (the zeros earlier the 1 are not pregnant). In addition, 120.00 has five significant figures since information technology has three trailing zeros. This convention clarifies the precision of such numbers. For example, if a measurement that is precise to four decimal places (0.0001) is given every bit 12.23, so the measurement might be understood as having but 2 decimal places of precision available. Stating the event every bit 12.2300 makes it articulate that the measurement is precise to four decimal places (in this instance, half dozen significant figures).
The number 0 has i meaning figure. Therefore, any zeros after the decimal signal are also meaning. Case: 0.00 has iii pregnant figures.
Any numbers in scientific notation are considered significant. For instance, 4.300 10 10^-4 has 4 pregnant figures.

Conventions Addressing Pregnant Figures

The significance of trailing zeros in a number not containing a decimal betoken can be ambiguous. For instance, it may not e'er exist clear if a number like 1300 is precise to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or doubt. Various conventions exist to address this outcome:

A bar may be placed over the last significant effigy, showing that any abaft zeros following this are insignificant. For case, 1300 with a bar placed over the starting time 0 would have 3 significant figures (with the bar indicating that the number is precise to the nearest x).
The concluding significant figure of a number may be underlined; for instance, "2000" has two significant figures.
A decimal signal may exist placed after the number. For instance "100." indicates specifically that three meaning figures are meant.
In the combination of a number and a unit the ambiguity tin be avoided by choosing a suitable unit prefix. For example, the number of significant figures in a mass specified as 1300 thou is ambiguous, while in a mass of xiii hg or 1.3 kg, it is much clearer.

When converting from decimal form to scientific annotation, always maintain the same number of significant figures. For example, 0.00012 has two significant figures, therefore the right scientific notation for this number would be 1.2 ten ten-⁴.

When multiplying and dividing numbers, the number of significant figures used is determined by the original number with the smallest amount of significant figures. When adding and subtracting, the final number should exist rounded to the decimal bespeak of the to the lowest degree precise number.

Examples:

1.423 x 4.2 = half dozen.0 since 1.423 has 4 significant figures and 4.2 simply has 2 significant figures, the final answer must besides have 2 significant figures.

234.67 – 43.five = 191.2 since 43.5 has one decimal place and 234.67 has two decimal places, the final respond must have just 1 decimal identify.

Another Manner to Determine Sig Figs: The Pacific Dominion & the Atlantic Rule

It can exist challenging to remember all the rules about significant figures and whether each aught is meaning or not pregnant. Here's another way to determine meaning figures (sig figs): the Pacific and Atlantic Rule.

If a number has a decimal Present, use the Pacific dominion (note the double P's). The Pacific Ocean is on the left side of the United States then start at the left side of the number. Start counting sig figs at the commencement not-nil number and continue to the end of the number. For example, since there is a decimal nowadays in 0.000560 starting time from the left side of the number. Don't start counting sig figs until the first non-cipher number (v), then count all the manner to the stop of the number. Therefore, there are 3 sig figs in this number (5,half-dozen,0).

If a number has no decimal (the decimal is Absent-minded) use the Atlantic rule (again, annotation the double A's). Since the Atlantic Body of water is on the correct side of the United States, start on the right side of the number and start counting sig figs at the first not-goose egg number. For case, since there is no decimal in 2900 start from the right side of the number and start counting sig figs at the first non zero number (9). Then there are ii sig figs in this number (ii,ix).

Significant Figures Made Easy! – YouTubeDon't be dislocated past significant figures. It will just make sense with this video. The video introduces significant figures and discusses how to round for multiplication and division using significant figures.