Which is greater, 0.26 or 0.206? And why? (أيهما أكبر، ٠.٢٦ أم ٠.٢٠٦؟ ولماذا؟)

0.26 is greater. When you compare digit by digit from the left, the ones place is the same (0) and the tenths place is the same (2). In the hundredths place, 6 is greater than 0. So, 0.26 > 0.206. (العدد ٠.٢٦ هو الأكبر. عند المقارنة من اليسار، خانة الآحاد (٠) والجزء من عشرة (٢) متساويتان. في خانة الجزء من مئة، ٦ أكبر من ٠. لذلك ٠.٢٦ > ٠.٢٠٦.)

How do you compare decimals with different numbers of digits, like 52.008 and 52.8? (كيف تقارن أعدادًا عشرية بعدد مختلف من الخانات، مثل ٥٢.٠٠٨ و ٥٢.٨؟)

Start by comparing from the largest place value. The whole numbers are the same (52). Next, compare the tenths place. In 52.008, the tenths digit is 0. In 52.8, the tenths digit is 8. Since 0 is less than 8, we know that 52.008 < 52.8. You can also add zeros to make them the same length: 52.008 vs 52.800. (ابدأ بالمقارنة من أكبر قيمة مكانية. العدد الصحيح متساوٍ (٥٢). بعد ذلك، قارن خانة الجزء من عشرة. في ٥٢.٠٠٨، الرقم هو ٠. وفي ٥٢.٨، الرقم هو ٨. بما أن ٠ أصغر من ٨، فإن ٥٢.٠٠٨ < ٥٢.٨. يمكنك أيضاً إضافة أصفار ليصبح لهما نفس الطول: ٥٢.٠٠٨ مقابل ٥٢.٨٠٠.)

Are 67.5 and 67.500 equal? (هل العددان ٦٧.٥ و ٦٧.٥٠٠ متساويان؟)

Yes, they are equal. Adding zeros to the end of a decimal number (after the last non-zero digit) does not change its value. 67.5 is the same as 67.50, which is the same as 67.500. (نعم، هما متساويان. إضافة أصفار في نهاية العدد العشري (بعد آخر رقم غير صفري) لا يغير من قيمته. ٦٧.٥ تساوي ٦٧.٥٠ وتساوي ٦٧.٥٠٠.)

Comparing Decimals (مقارنة الكسور العشرية) | Grade 5 Lesson

Q: Are 67.5 and 67.500 equal? (هل العددان ٦٧.٥ و ٦٧.٥٠٠ متساويان؟)

Yes, they are equal. Adding zeros to the end of a decimal number (after the last non-zero digit) does not change its value. 67.5 is the same as 67.50, which is the same as 67.500. (نعم، هما متساويان. إضافة أصفار في نهاية العدد العشري (بعد آخر رقم غير صفري) لا يغير من قيمته. ٦٧.٥ تساوي ٦٧.٥٠ وتساوي ٦٧.٥٠٠.)

Learn: How to Compare Two Decimals

You can use place-value charts to compare decimals. The main rule is to always begin with the digit in the greatest place value.

Example A: Compare $2.948$ and $2.957$

Place value chart for 2.948 and 2.957 | Math Egypt by Mr. Ayman Hassan (جدول القيمة المكانية للعددين 2.948 و 2.957 | ماث إيجيبت - مستر ايمن حسن)

Compare ones: $2 = 2$ ones. They are the same.
Compare tenths: $9 = 9$ tenths. They are the same.
Compare hundredths: $4 < 5$ hundredths. We found a difference!

So, $2.948 < 2.957$

Example B: Compare $0.26$ and $0.206$

Place value chart for 0.26 and 0.206 | Math Egypt by Mr. Ayman Hassan (جدول القيمة المكانية للعددين 0.26 و 0.206 | ماث إيجيبت - مستر ايمن حسن)

Compare ones: $0 = 0$ ones.
Compare tenths: $2 = 2$ tenths.
Compare hundredths: $6 > 0$ hundredths. We found the difference!

So, $0.26 > 0.206$

Notes for parents: Remind your child to begin comparing with the greatest place value.

Strategy 2: Step-by-Step Comparison

You can also compare by lining up the decimal points and comparing the digits from left to right.

Example: Compare $2.135$ and $2.137$

Step-by-step comparison of 2.135 and 2.137 | Math Egypt by Mr. Ayman Hassan (مقارنة خطوة بخطوة للعددين 2.135 و 2.137 | ماث إيجيبت - مستر ايمن حسن)

So, $2.135 < 2.137$

Example 1

Compare: 52.008 and 52.8

Solution

Example 2

Compare using "<", "> or =".

a. Compare $0.395$ and $\frac{385}{1000}$

b. Compare "28 thousandths" and $0.28$

c. Compare "4 ones, 4 hundredths, 5 thousandths" and $4.054$

Solution

a. Since $\frac{385}{1000} = 0.385$
So, $0.395 > 0.385$

b. Since "28 thousandths" = $0.028$
So, $0.028 < 0.28$

c. Since "4 ones, 4 hundredths, 5 thousandths" = $4.045$
So, $4.045 < 4.054$

Example 3

Compare using "<", "> or =".

a. $3.204$ ___ $3.24$

b. $19.2$ ___ $19.200$

c. $20.7$ ___ $20.077$

d. $1.01$ ___ $1.099$

e. $9.08$ ___ $9.079$

f. $14.010$ ___ $14 \frac{9}{10}$

g. $4.12$ ___ $4 + 0.1 + 0.007$

h. "5 thousandths" ___ $0.500$

Solution

a. Since $3.24$ can be written as $3.240$
So, $3.204 < 3.240$

b. Since $19.200$ is equivalent to $19.2$
So, $19.2 = 19.200$

c. Since $20.7$ can be written as $20.700$
So, $20.700 > 20.077$

d. Since $1.01$ can be written as $1.010$
So, $1.010 < 1.099$

e. Since $9.08$ can be written as $9.080$
So, $9.080 > 9.079$

f. Since $14 \frac{9}{10} = 14.9$
So, $14.010 < 14.9$

g. Since $4 + 0.1 + 0.007 = 4.107$
So, $4.12 > 4.107$

h. Since "5 thousandths" = $0.005$
So, $0.005 < 0.500$

Example 4

Compare the numbers using ">", "<" or "=".

a. $2.71$ ___ $2 \frac{8}{100}$

b. $2.007$ ___ $7 \frac{2}{1000}$

c. $1.002$ ___ $\frac{1002}{1000}$

d. $16.24$ ___ $16 \frac{224}{1000}$

e. $4.000$ ___ $\frac{400}{1000}$

f. $99.257$ ___ "1,234 tenths"

g. "3 thousandths" ___ $\frac{30}{100}$

h. "Eighteen thousandths" ___ $0.02$

i. "8 tenths" ___ $0.799$

j. $0.402$ ___ "402 thousandths"

Solution

a. Since $2 \frac{8}{100} = 2.08$
So, $2.71 > 2.08$

b. Since $7 \frac{2}{1000} = 7.002$
So, $2.007 < 7.002$

c. Since $\frac{1002}{1000} = 1.002$
So, $1.002 = 1.002$

d. Since $16 \frac{224}{1000} = 16.224$
So, $16.24 > 16.224$

e. Since $\frac{400}{1000} = 0.400$
So, $4.000 > 0.400$

f. Since "1,234 tenths" = $123.4$
So, $99.257 < 123.4$

g. Since "3 thousandths" = $0.003$ and $\frac{30}{100} = 0.30$
So, $0.003 < 0.30$

h. Since "Eighteen thousandths" = $0.018$
So, $0.018 < 0.02$

i. Since "8 tenths" = $0.8$
So, $0.8 > 0.799$

j. Since "402 thousandths" = $0.402$
So, $0.402 = 0.402$

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Lesson 4: Comparing Decimals