Multiplication and division of decimals by 10, 100, 1000 ...
Mnożenie liczb dziesiętnych przez 10, 100, 1000, …
Learning objectives
You will learn to multiply and divide decimal fractions by 10, 100, 1000 ...
Learning effect
You multiply and divide decimal fractions by 10, 100, 1000 ...
Introduction. In your notebook write the numbers 1234,5678 and 56789. Using the calculator, calculate the results of multiplication and divisiondivision of these numbers by 10, 100 and 1000. Compare the location of the decimal pointdecimal point in the numbers and their results in each case.
Open the slideshow and observe the change in the position of the decimal pointdecimal point as a result of multiplying decimals by 10, 100, 1000 ... After finishing the task present the results of your observations.
Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/D14d0php9
Conclusions:
To multiplymultiply a decimal fraction by 10, 100, 1000 ... it is enough to move the decimal pointdecimal point to the right in the multiplied number by as many places as there are zeros in the number by which we multiply.
Multiplying decimals by 10, 100, 1000 ..., sometimes we have to expand them and add zero at the end.
In some cases, after moving the decimal pointdecimal pointdecimal point, zeros written to the left of the number that we multiplymultiply should be omitted.
Open the slideshow and observe the position of the decimal pointdecimal point when dividing decimals by 10, 100, 1000 ... After finishing the task, present the results of your observations.
Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/D14d0php9
Conclusions:
In order to divide a decimal fraction by 10, 100, 1000 ... it is enough to move the decimal pointdecimal point to the left side, by as many places as there are zeros in the number by which we divide (divisor).
Dividing decimals by 10, 100, 1000 ..., we must in some cases add zero to the left side of the dividend or omit unnecessary zeros on the right side of the dividend.
Do the calculations applying the rules you have learned. Do the task as fast as you can. Check your calculation results with the calculator.
Level A | Level B | Level C | Level D |
a) 3,27 · 10 | a) 0,3 · 100 | a) 321,54 : 100 | a) 4,5 : 10 |
Answer the questions below using the information presented in the tables.
Name of commodity | Price for a kilo | Name of commodity | Price |
Beef meat | 32,50 zł | A loaf of bread | 2,35 zł |
Pork ham | 12,40zł | A roll 1 szt, | 0,35 zł |
Sausages | 13,99 zł | A Packet of butter | 7,65 zł |
Cottage cheese | 9,85 zł | Carton of milk1 l | 2,19 zł |
a) How much do you have to pay for 10 kg of cottage cheese?
b) How much do you have to pay for 10 liters of milk?
c) How much do you have to pay for 100 rolls?
d) What is the price of 10 decagrams of ham?
e) How much does 1 decagram of butter cost?
f) School canteen bought 10 packets of butter, 100 rolls and 10 loaves of bread. How much did the school canteen pay for the shopping?
g) The store sold: 100 kg of beef, 100 kg of ham, 100 kg of sausages and 10 kg of cottage cheese. What is the total value of the goods sold?
Kasia bought 10 decagrams of sweets for PLN 28.50 per 1 kg.
Calculate how much the girl paid for her sweets.
Remember:
To multiplymultiply a decimal fraction by 10, 100, 1000 ... it is enough to move the decimal pointdecimal point to the right in the multiplied number by as many places as there are zeros in the number by which we multiply.
Multiplying decimals by 10, 100, 1000 ..., sometimes we have to expand them and add zero at the end.
In some cases, after moving the decimal pointdecimal point, zeros written to the left of the number that we multiplymultiply should be omitted.
In order to divide a decimal fraction by 10, 100, 1000 ... it is enough to move the decimal pointdecimal point to the left side, by as many places as there are zeros in the number by which we divide (divisor).
Dividing decimals by 10, 100, 1000 ..., we must in some cases add zero to the left side of the dividend or omit unnecessary zeros on the right side of the dividend.
Do the revision exercises.
Exercises
Determine which sentences are true.
- The number 5243,6 is 10 times greater than 524,36.
- The number 5,2436 is 100 times greater than 524,36.
- The number 5,2436 is 10 times smaller than 524,36.
- The number 5,2436 is 100 times smaller than 524,36.
Replace x with the appropriate number:
a) 247,876 · x = 24787,6
b) 98,7654 : x = 9,87654
c) 246,875 · x = 246875
d) 34,5621 : x = 0,34521
Peter's uncle's car uses 9 liters of petrol per 100 km.A liter of petrol costs PLN 4,90.
How much will Peter’s uncle pay for the petrol needed to drive his car for 1000 km?
How much does the fuel needed to drive 1 km cost? Write the solutions in English.
Indicate which pairs of expressions or words are translated correctly.
- przesuwanie przecinka - moving the decimal point
- pomijanie zera - omitting zero
- dopisywanie zera - simplifying decimal fractions
- skracanie ułamków dziesiętnych - adding zero
- dopisywanie zera
- pomijanie zera
- moving the decimal point
- przesuwanie przecinka
- adding zero
- omitting zero
- simplifying decimal fractions
- rozszerzanie ułamków dziesiętnych
- expanding decimal fractions
- skracanie ułamków dziesiętnych
Glossary
mnożenie
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: multiply
dzielenie
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: division
ułamek dziesiętny
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: decimal fractions
przecinek dziesiętny
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: decimal point
mnożenie ułamków dziesiętnych przez 10, 100, 1000 ...
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: multiplication of decimals by 10, 100, 1000 ...
pomijanie zera
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: omitting zero
skracanie ułamków dziesiętnych
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: simplifying decimal fractions
Keywords
decimal fractionsdecimal fractions
multiplication of decimals by 10, 100, 1000 ...multiplication of decimals by 10, 100, 1000 ...
simplifying decimal fractionssimplifying decimal fractionssimplifying decimal fractions