SparkPrep GMAT Quant Module 02: Digits Decimals

1. Spark Prep SG - GMAT
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Digits, Decimals,
Powers of 10
Spark Prep - GMAT
6-0.12 : 3-0.12

2. Spark Prep SG - GMAT
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Confidential and proprietary. Not to be distributed without permission.
Learning Objectives
By the end of this module, you should:
➢ Know how GMAT defines Digits, Integers and Decimals
➢ Know Place Value, Powers of 10 and Scientific notation
➢ Be able to use Powers of 10 to simplify problems

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* Most of the following concepts will seem basic to you, but it’s good to review because
GMAT questions can take advantage of nuances and exceptions.
● Digits are the fundamental building blocks of the numbers in our arithmetic system. All
numbers are made up of the following digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
● A number can be categorized either as an Integer or as a Decimal.
● An Integer is a whole number that can contain any number of digits. For example, the
number 7 is a single digit Integer, while the number 723 is a three-digit Integer.
● A Decimal is not an integer and is located between two integers on the number line.
For example, 7.5 is a decimal located halfway between the integers 7 and 8.
What are Digits, Integers and Decimals?

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Place Value
3
Hundred
thousands
7
Ten
thousands
1
Thousands
3
Hundreds
9
Tens
3
Ones
6
Millions
9
Thousandths
6
Hundredths
7
Tenths
● Each digit in a number occupies a position called a place value. Let’s look at the place
values in the number 6,371,393.769
, ,
.
● As you move from one place value to another, you are either going up or down by
powers of 10.

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Confidential and proprietary. Not to be distributed without permission.
Place Value and Powers of 10
● Let’s start with the number 4 and increase it by powers of 10 each time:
4
X 10
40
X 10
400
X 10
4,000
● As we multiply by 10 each time, the digit 4 moves up one place value. For this reason,
we can express 4000 as 4 x 103 since 4 has moved 3 place values in this case from the
units place to the thousands place.

6. Spark Prep SG - GMAT
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Confidential and proprietary. Not to be distributed without permission.
Practice Problem
If m is an integer and 0.00020101 x 10m is
greater than 2,000, what is the least possible
value of m?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

7. Spark Prep SG - GMAT
Copyright QL Education, Ltd. Pte.,
Confidential and proprietary. Not to be distributed without permission.
Practice Problem
If m is an integer and 0.00020101 x 10m is
greater than 2,000, what is the least possible
value of m?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
In order for 0.00020101 x 10m to be greater than 2,000,
the decimal must move at least 7 places to the right.
So the least possible value of m is 7.
Answer is D

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Confidential and proprietary. Not to be distributed without permission.
More on Powers of 10...
● Essentially any number can be expressed as a number multiplied by a power of 10.
Scientific notation is based on this principle - it allows us to express very large
numbers in a more succinct form - as a number between 1 and 10 multiplied by a
power of 10.
● Let’s take the distance of the earth from the sun, which is 149,600,000 km. To do this,
simply place the decimal point between the first and second non-zero digits in the
number (1 and 4 in this case) and count how many place values you need to move the
decimal point to arrive at the original number (8 place values in this case). The number
of place values moved corresponds to the power of 10 in the scientific notation.
● The number 149,600,000 can therefore be expressed as 1.496 x 108 .

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Confidential and proprietary. Not to be distributed without permission.
Practice Problem
If , then n - h =
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

10. Spark Prep SG - GMAT
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Practice Problem
If , then n - h =
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Simplify the equation by eliminating the fraction. Multiply
both sides by the denominator:
0.0012 x 10n = 0.12 x 10h+7
Put both sides in proper scientific notation by adjusting
the powers of 10 on each side. You can move the decimal
place to a coefficient so long as you take away
corresponding power of 10s.
0.0012 x 10n = 1.2 x 10n-3 and 0.12 x 10h+7 = 1.2 x 10h+6
1.2 x 10n-3 = 1.2 x 10h+6
n - 3 = h + 6 ---> n - h = 9
Answer is A

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Practice Problem (alternative solution)
If , then n - h =
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Simplify the equation by eliminating the fraction. Multiply
both sides by the denominator:
0.0012 x 10n = 0.12 x 10h+7
Make coefficients on both sides the same by changing the
right side. Decrease 0.12 by 10-2 while increasing the
power of 10h+7 to 10h+9.
0.0012 x 10n = 0.12(10-2)x10h+7(102)
0.0012 x 10n = 0.0012 x 10h+9
n = h + 9, n - h = 9
Answer is A

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Confidential and proprietary. Not to be distributed without permission.
Summary
● Digits, Integers and Decimals
○ Digits are the building blocks of numbers
○ Integers are whole numbers with no decimals or fractions
○ Decimal is a number between two integers on a number line
● Place Values
○ Moving left from the decimal point are ones, tens, hundreds,...
○ Moving right from the decimal point are tenths, hundredths, thousandths,...
○ Move decimal places and correspondingly adjust powers of 10 to a term to bring two sides of
an equation closer to each other