Use exponential notation to express the number 385,500 to a. one significant figure. b. two sign

Use exponential notation to express the number 385,500 to a....

Key Concepts

Significant Figures

Significant figures refer to the digits in a number that contribute to its precision. They include all non-zero digits, and any zeros that are significant based on their position. When representing numbers using significant figures, careful rounding is necessary to retain only the desired number of meaningful digits while accurately reflecting the magnitude of the number.

Rounding Rules

Rounding rules are applied to reduce the number of digits in a number and to express it with a given precision, such as a specific number of significant figures. These rules dictate when digits should be increased or left unchanged based on the value of the digits that are being removed. Consistent application of rounding rules ensures that the approximated value closely represents the original number's scale and magnitude.

Scientific Notation

Scientific notation, also known as exponential notation, is a method of writing numbers that are too large or too small in a compact form. It expresses a number as the product of a coefficient (a number between 1 and 10) and a power of 10. This format is especially useful for clearly highlighting the scale of a number and for performing calculations involving very large or very small values.

Transcript

00:01 Okay, so this question is trying to get you used to understanding scientific notation and being able to express different numbers or expressed numbers in different forms of scientific notation based on how many certificates figures the problem is asking for.

00:17 Right.

00:17 So this problem wants you to translate 385,504 um, four different forms of scientific notation that have different significant figures.

00:29 So with regards to a one significant figure, right.

00:32 So this number right now has four.

00:34 Because there's no decimal here.

00:36 So all the non zero numbers are significant, which is four numbers here.

00:40 If there were a decimal point than these would be, um, you should be leading zeros, right? so that would make beast to zero significance.

00:49 Overall, we'd have sex.

00:50 That's not the case here.

00:51 That's not even the problem.

00:53 I'm just trying to help you out.

00:54 Um, if we want to express this number within one significant figure in scientific notation, we'd have to round this number up, right? so in order for this number to have one significant figure, we would have to round it up.

01:06 Let me get my pen.

01:07 We have to round it up to 400 thousands, which was no decimal point after this number would only have one significant figure before, right? but because we have to express it in scientific notation, we have to use our, um we have to multiply it by 10 to some power.

01:26 And we're gonna get that power from counting back from where the decimal would be, right, until we reach the point where the number would be between one and 10.

01:37 That's the rule.

01:37 It's on a deputation, right? so if we count 12345 that would give me four times 10 to the fifth.

01:46 So we're multiplying four by 100,000 to get the foreign thousands.

01:51 If i put a decimal point here in at a zero, that would be two significant figures.

01:55 That's actually an answer to the next problem, right? so i can write what i just said.

01:59 You could express that same number as 4.0 times 10 to the fifth, or you could around in this number differently.

02:07 You could round it upward or here, so we don't think confucius weaken around this number differently so we could round it to, let's say, 390 thousands, which also has three.

02:19 Significant to stiffy and figures...

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