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Rounding decimal numbers
Decimal numbers are rounded similarly as natural numbers.
- Determine to which place value you round.
- You round down if the digit at the next place value is \latex{ 0, } \latex{ 1, } \latex{ 2, } \latex{ 3 } or \latex{ 4 }.
- You round up if the digit at the next place value is \latex{ 5, } \latex{ 6, } \latex{ 7, } \latex{ 8 } or \latex{ 9 }.
ROUNDING TO TENTHS
ROUNDING TO HUNDREDTHS
\latex{ 2.135 } rounded to tenths is \latex{ 2.1 }.
So \latex{ 2.135 } with one decimal place accuracy is \latex{ 2.1 }.
So \latex{ 2.135 } with one decimal place accuracy is \latex{ 2.1 }.
When rounding the numbers marked on the number line to the nearest tenth, you get \latex{ 2.1 .}
\latex{ 2.135 } rounded to hundredths is \latex{ 2.14 }.
So \latex{ 2.135 } with two decimal accuracy is \latex{ 2.14 }.
So \latex{ 2.135 } with two decimal accuracy is \latex{ 2.14 }.
When rounding the numbers marked on the number line to the nearest hundredth, you get \latex{ 2.14 }.
\latex{ 2.0 }
\latex{ 2.05 }
\latex{ 2.1 }
\latex{ 2.15 }
\latex{ 2.13 }
\latex{ 2.135 }
\latex{ 2.14 }
\latex{ 2.145 }
The accuracy of measurements
The workers dig a \latex{ 1.5 } \latex{ m } deep hole.
Silvia’s height was measured to be \latex{ 150 } \latex{ cm } by the school nurse.
The glazier cut a piece of glass that was \latex{ 1,500 } \latex{ mm } long.
Silvia’s height was measured to be \latex{ 150 } \latex{ cm } by the school nurse.
The glazier cut a piece of glass that was \latex{ 1,500 } \latex{ mm } long.
These values expressed in \latex{ metres }: depth of the hole: \latex{ 1.5 } \latex{ m }; Silvia's height: \latex{ 1.50 } \latex{ m }; the length of the glass: \latex{ 1.500 } \latex{ m }.
In the case of Silvia's height and the length of the glass, the zeros cannot be eliminated from the end of the numbers because these indicate that Silvia's height was measured in \latex{ centimetres } (two decimal place accuracy), while the length of the glass in \latex{ millimetres } (three decimal place accuracy).
Exercises
{{exercise_number}}. Round the following decimal numbers to the nearest tenth (one decimal place).
a) \latex{ 4.738 }
b) \latex{ 1.2595 }
c) \latex{ 10.267 }
d) \latex{ 2.087 }
e) \latex{ 15.509 }
f) \latex{ 35.3535 }
g) \latex{ 0.075 }
h) \latex{ 140.0498 }
i) \latex{ 20.00795 }
j) \latex{ 42.988 }
{{exercise_number}}. Round the following decimal numbers to the nearest hundredth (two decimal places).
a) \latex{ 3.428 }
b) \latex{ 1.8791 }
c) \latex{ 10.854 }
d) \latex{ 8.084 }
e) \latex{ 17.709 }
f) \latex{ 25.2729 }
g) \latex{ 0.047 }
h) \latex{ 130.0398 }
i) \latex{ 80.70497 }
j) \latex{ 5.0449 }
{{exercise_number}}. Using a digital thermometer, Peter’s body temperature is \latex{ 36.68 }\latex{ °C }. What value would a traditional thermometer show if it is accurate to only one decimal place?
{{exercise_number}}. In \latex{ 2024 }, Lewis Hamilton won the Formula \latex{ 1 } British Grand Prix, crossing the finish line \latex{ 1.485 } \latex{ seconds } before Max Verstappen, who finished in second place. In a magazine, the gap between them was published rounded to the nearest hundredth, while another rounded it to the nearest tenth. What time gap was published in the magazines?
{{exercise_number}}. The thickness of a fishing line is \latex{ 0.196 } \latex{ millimetres }. What is the thickness of the fishing line rounded to the nearest hundredth (two decimal places)?
{{exercise_number}}. Round the following decimal numbers to the nearest tenth and the nearest whole number.
a) \latex{ 4.2 }
b) \latex{ 3.58 }
c) \latex{ 9.499 }
d) \latex{ 12.58 }
e) \latex{ 19.07 }
f) \latex{ 20.499 }
g) \latex{ 780.5 }
h) \latex{ 34.725 }
i) \latex{ 199.51 }
j) \latex{ 39.999 }
{{exercise_number}}. The weight of a salami stick is \latex{ 1.796 } \latex{ kg }. Round it to the nearest whole number, the nearest tenth, and the nearest hundredth.
{{exercise_number}}. Zoe and Lou weighed their backpacks. Zoe’s backpack is \latex{ 7 } and a half \latex{ kg }, Lou’s is \latex{ 7.05 } \latex{ kg }. Which backpack was heavier?
{{exercise_number}}. The longest blue whale measured \latex{ 33.58 } \latex{ metres }. What is the length of the animal
a) rounded to the nearest whole number;
b) expressed in \latex{ decimetres? }
{{exercise_number}}. The largest male elephant was found in \latex{ 1974 } and weighed \latex{ 12.24 } \latex{ tonnes }. Round its body mass to
a) the nearest whole number;
b) the nearest tenth (one decimal place).
{{exercise_number}}.
a) What is the smallest number that must be rounded to \latex{ 4 }?
b) What is the smallest number that must be rounded to \latex{ 5 }?
c) Mark the numbers that must be rounded to \latex{ 4 } on a number line.
d) Mark the numbers that must be rounded to \latex{ 5 } on a number line.
b) What is the smallest number that must be rounded to \latex{ 5 }?
c) Mark the numbers that must be rounded to \latex{ 4 } on a number line.
d) Mark the numbers that must be rounded to \latex{ 5 } on a number line.
{{exercise_number}}.
a) What is the smallest number that must be rounded to \latex{ 7.4 }?
b) What is the smallest number that must be rounded to \latex{ 7.5 }?
c) Mark the numbers that must be rounded to \latex{ 7.4 } on a number line.
d) Mark the numbers that must be rounded to \latex{ 7.5 } on a number line.
b) What is the smallest number that must be rounded to \latex{ 7.5 }?
c) Mark the numbers that must be rounded to \latex{ 7.4 } on a number line.
d) Mark the numbers that must be rounded to \latex{ 7.5 } on a number line.
{{exercise_number}}. Mark the numbers that must be rounded to \latex{ 9.81 } on a number line.
{{exercise_number}}. Anna says that a rod is shorter than \latex{ 1.6 } \latex{ m }, while Ben claims it is not shorter than one and a half \latex{ metres. } How long can the rod be if both children are right?
{{exercise_number}}. The daily turnover of a supermarket rounded to the nearest tenth was \latex{ 52.8 } thousand \latex{ euros. } How many \latex{ euros } was its income?
{{exercise_number}}. The length of a room rounded to a whole number is \latex{ 6 } \latex{ metres. } What could the length of the room be in \latex{ decimetres } and \latex{ centimetres? }
{{exercise_number}}. Hank, the fisherman, bragged that the fish he had caught weighed \latex{ 10 } \latex{ kilograms }, rounded to the nearest whole number. How many \latex{ dekagrams } could the weight of the fish be?
{{exercise_number}}. How many \latex{ dekagrams } can the apples weigh if the scale at the market shows \latex{ 2.8 } \latex{ kg }? (The scale is accurate to one decimal place.)
{{exercise_number}}. The longest anaconda ever found was \latex{ 9.6 } \latex{ m } long. How long could it measure in \latex{ decimetres } and \latex{ centimetres ?}
{{exercise_number}}. On a floor plan, the length of a square-shaped room was marked \latex{ 4.00 } \latex{m }. What do the two zeros after the decimal point express? How much skirting is needed if the door of the room is \latex{ 0.90 } \latex{ m } wide?
{{exercise_number}}. Match the objects with the corresponding values.
A) Weight of paper collected by a class
(\latex{ 1 }) \latex{ 9.5 } \latex{ m }
B) The maximum load-bearing capacity of a lift
(\latex{ 2 }) \latex{ 473.5 } \latex{ kg }
C) The distance of a marathon
(\latex{ 3 }) \latex{ 0.20 } \latex{ l }
D) The distance between London and Reading
(\latex{ 4 }) \latex{ 67 } \latex{ km }
E) The long jump record in \latex{ 2024 }
(\latex{ 5 }) \latex{ 200 } \latex{ ml }
F) The length of a classroom
(\latex{ 6 }) \latex{ 8.95 } \latex{ m }
G) A cup of milk
(\latex{ 7 }) \latex{ 480 } \latex{ kg }
H) A small box of apple juice
(\latex{ 8 }) \latex{ 42.195 } \latex{ km }
Quiz
What is the smallest number that gives \latex{ 5.60 } when rounded to the nearest hundredth?
