### All HiSET: Math Resources

## Example Questions

### Example Question #1 : Numbers And Operations On Numbers

How many significant digits does the number 205,000 have?

**Possible Answers:**

Four

Five

Six

Two

Three

**Correct answer:**

Three

The number of significant digits that an integer has is equal to the number of digits from its first nonzero digit to its last nonzero digit, inclusive. As seen below in boldface, this is a group of three digits:

**205**,000

Three is the correct response.

### Example Question #1 : Numbers And Operations On Numbers

How many significant digits does the number 0.03040 have?

**Possible Answers:**

Six

Five

Four

Two

Three

**Correct answer:**

Four

In a decimal expression, any leading zeroes of a decimal expression must be discounted as significant digits; all digits from the first nonzero digit onward must be counted. These digits are in boldface below:

0.0**3040**

Four is the correct response.

### Example Question #1 : Precision

How many significant digits does the number 60.000007 have?

**Possible Answers:**

Eight

Two

Four

One

Six

**Correct answer:**

Eight

To find the number of significant digits of a decimal expression with digits on both sides of the decimal point, count the digits from the first (nonzero) digit to the last digit. 60.000007 has eight digits, all of which are significant.

### Example Question #4 : Numbers And Operations On Numbers

How many significant digits does the number 0.080808080 have?

**Possible Answers:**

Four

Five

Nine

Eight

Ten

**Correct answer:**

Eight

In a decimal expression, any leading zeroes of a decimal expression must be discounted as significant digits; all digits from the first nonzero digit onward must be counted. These digits are in boldface below:

0.0**80808080 **

The figure has eight significant digits.

### Example Question #5 : Numbers And Operations On Numbers

Multiply, adjusting for *significant digits.*

**Possible Answers:**

**Correct answer:**

First, determine the number of significant digits in each factor. Since each factor includes only nonzero digits, the number of significant digits in each is simply equal to the number of digits. Thus, **7.21** and **2.713** have three and four significant figures, respectively.

Now, multiply the numbers outright. The product is

The product must be rounded to the appropriate number of significant digits. This number must be the lesser of the numbers of significant digits that appear in the factors, which is three. Count from the first nonzero digit:

Rounded, this is 19.6, the correct response.

### Example Question #6 : Numbers And Operations On Numbers

Multiply, adjusting for *significant digits.*

**Possible Answers:**

**Correct answer:**

First, determine the number of significant digits in each factor. Each factor has one or more leading zeroes, and each has its final digit after the decimal point, so in each case, the number of significant digits is equal to the number of digits from the first nonzero digit to the last digit. 0.0**456** and 0.**53** have three and two significant digits, respectively.

Now, multiply the numbers outright. The product is

The product must be rounded to the appropriate number of significant digits. This number must be the lesser of the numbers of significant digits that appears in the factors, which is two. Count from the first nonzero digit:

Rounded, this is 0.24, the correct response.

### Example Question #7 : Numbers And Operations On Numbers

Multiply, adjusting for *significant digits.*

**Possible Answers:**

**Correct answer:**

First, determine the number of significant digits in each factor. Both factors have leading zeroes, which must be discounted. Therefore, in each factor, the number of significant digits can be found by counting from the first nonzero digit to the final digit. 0.00**421** and 0.00**332** each have three significant digits.

Now, multiply the numbers outright. The product, ignoring any trailing zeroes, is

The product must be rounded to the appropriate number of significant digits. This number must be the lesser of the numbers of significant digits that appears in the factors, which is three. Count from the first nonzero digit:

Rounded, this is 0.0000140, the correct choice. (Note that this trailing zero must be kept in order to have three significant digits.)

### Example Question #8 : Numbers And Operations On Numbers

Add, adjusting for *significant digits:*

**Possible Answers:**

**Correct answer:**

When adding numbers, accounting for significant digits, the sum must be rounded to the same place as the least precise of the numbers. 9.700**0** and 4.8**1** have their final digits in the ten-thousandths and hundredths place, respectively; this makes 4.81 the less precise measurement, and the sum must be rounded to the nearest hundredth.

Now, add the numbers outright:

To the nearest hundredth, this is rounded down to 14.58, the correct response.

### Example Question #9 : Numbers And Operations On Numbers

Subtract, adjusting for *significant digits:*

**Possible Answers:**

**Correct answer:**

When subtracting numbers, accounting for significant digits, the difference must be rounded to the same place as the least precise of the numbers. 17.**3** and 13.45**2** have their final digits in the tenths and thousandths place, respectively; this makes 17.3 the less precise measurement, and the difference must be rounded to the nearest tenth.

Now, subtract the numbers outright, and round to the nearest tenth.

To the nearest tenth, this is rounded down to 3.8, the correct response.

### Example Question #10 : Numbers And Operations On Numbers

Multiply, adjusting for *significant digits.*

**Possible Answers:**

**Correct answer:**

First, determine the number of significant digits in each factor. Both factors have leading zeroes, which must be discounted, and trailing zeroes after the decimal point, which must be counted; therefore, in each factor, the number of significant digits can be found by counting from the first nonzero digit to the final digit. 0.**660** and 0.**5550** have three and four significant digits, respectively.

Now, multiply the numbers outright. The product, ignoring any trailing zeroes, is

The product must be rounded to the appropriate number of significant digits. This number must be the lesser of the numbers of significant digits that appear in the factors, which is three. Count from the first nonzero digit:

Rounded, this is 0.366, the correct choice.

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